Mathematics
Two alternate sides of a regular polygon, when produced, meet at right angle. Find :
(i) the value of each exterior angle of the polygon;
(ii) the number of sides in the polygon.
Rectilinear Figures
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Answer
(i) Let AB and CD be the alternate sides of regular polygon.
Given,
Two alternate sides of a regular polygon, when produced, meet at right angle.
We know that,
Interior angles of regular polygon are equal.
∴ ∠ABC = ∠BCD
⇒ 180° - ∠ABC = 180° - ∠BCD
⇒ ∠PBC = ∠BCP = x
In △ PBC,
⇒ ∠PBC + ∠BCP + ∠BPC = 180°
⇒ x + x + 90° = 180°
⇒ 2x = 180° - 90°
⇒ 2x = 90°
⇒ x =
⇒ x = 45°.
∴ ∠PBC = ∠BCP = 45°.
Hence, value of each exterior angle of the polygon = 45°.
(ii) By formula,
Number of sides in polygon = = 8.
Hence, number of sides in the polygon = 8.
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Related Questions
Assertion (A): In parallelogram ABCD, PD bisects ∠ADC and PC bisects angle DCB, then ∠DPC = 90°.
Reason (R): ∠PDC = x ∠ADC
∠PCD = x ∠BCD
∠PDC + ∠PCD = x (∠ADC + ∠BCD)
A is true, but R is false.
A is false, but R is true.
Both A and R are true, and R is the correct reason for A.
Both A and R are true, and R is the incorrect reason for A.
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